Studying Co-movements in Large Multivariate Models Without Multivariate Modelling

We propose an approach for checking the data admissibility of non-stationary multivariate time series models (VAR or VARMA) through that of their implied individual ARIMA specifications. In particular we show that the presence of different kinds of common cyclical features restrictions, leading to reduced rank in the short-run dynamics, explains why we identify parsimonious univariate ARIMA models in applied research, a paradox that the profession had difficulties to explain. We develop a new strategy for studying interactions between variables prior to possibly modelling them in a multivariate setting. Indeed, we provide tools to study features of individual time series with the aim to infer features of the complete system, as individual series keep a print of the system as a whole. The similarity of the autoregressive roots will be informative about co-movements existing in a vector autoregressive model as well as convergence between series for different economies. It will allow us to forecast series, to build business cycle indices, to unravel trends from cycles in a way that is consistent with the full multivariate system. Our results justify both the use of an homogeneous panel with hetegoneous cross-correlated vector moving average (VMA) errors and a factor structure, and the cross-sectional aggregation of ARIMA series. The advantages of our approach are many: 1) determining co-movements also when we cannot work with a complete system, 2) enhancing the accuracy of forecasts, 3) the ease of its implementation in complex situations, 4) the potential empirical studies in many fields.